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Long Division

Here's another one:

( 14x^4 - 5x^3 - 11x^2 - 11x + 8 ) / ( 2x - 1 )

Set it up:

divide 2x into 14x^4
                                                  14x^4 / 2x = 7x^3

Put the 7x^3 in its place.

Get out a piece of paper and work along with me on this!


step 1: multiply 7x^3 to ( 2x - 1 ) ... step 2: subtract the product ( 14x^4 - 7x^3 ), giving 2x^3 ... step 3: bring -11x^2 down, giving 2x^3 - 11x^2 ... step 4: divide 2x into 2x^3
                                                                           2x^3 / 2x = x^2

step 1: multiply x^2 to ( 2x - 1 ) ... step 2: subtract the product ( 2x ^3 - x^2 ) from the 2x^3 - 11x^2 we got in the last step, giving -10x^2 ... step 3: bring the -11x down, giving -10x^2- 11x ... step 4: divide 2x into -10x^2
                                                  -10x^2 / 2x = -5x